

Here and in what follows, we use the 'ket' operator \( \mathinner {|{\cdot }\rangle } \)  notation to indicate a column vector of any variable defined for the lattice velocity set, while \(\dagger \)  refers to the transpose operation. The combination of the monomials of the form \(\mathinner {|{e_x^m e_y^n}\rangle }\) , where \(m\)  and \(n\)  are integers, then defines the following set of natural or non-orthogonal basis vectors for the D2Q9 lattice: [1]}, [2]}
\( \mathbf {\mathsf {T}}= \Big [\; \mathinner {|{1}\rangle }, \mathinner {|{e_{x}}\rangle }, \mathinner {|{e_{y}}\rangle }, \mathinner {|{e_{x}^2+e_{y}^2}\rangle }, \mathinner {|{e_{x}^2-e_{y}^2}\rangle }, \mathinner {|{e_{x} e_{y}}\rangle }, \mathinner {|{e_{x}^2 e_{y}}\rangle }, \mathinner {|{e_{x} e_{y}^2}\rangle }, \mathinner {|{e_{x}^2 e_{y}^2}\rangle } \Big ],\) 
